On multi-Jensen functions and Jensen difference

Abstract

In this paper we characterize multi-Jensen functions f : Vn → W, where n is a positive integer, V, W axe commutative groups and V is uniquely divisible by 2. Moreover, under the assumption that f : ℝ → ℝ is Borel measurable, we obtain representation of f (respectively, f, g, h : ℝ → ℝ) such that the Jensen difference 2f (x+y/2) - f(x) - f(y) (respectively, the Pexider difference 2f (x+y/2) - g(x) - h(y)) takes values in a countable subgroup of ℝ. © 2008 The Korean Mathematical Society.